Question

The ratio between the length and breadth of a rectangular park is $3:2$. If a man cycling along the boundary of the park at the speed of $12$ km/hr completes one round in $8$ minutes, then the area of the park.

Answer 1

Perimeter $=$ Distance covered in $8$m

Distance$=$ speed $\times$ time

$=12\times \frac{8}{60}$

$=1.6$km

$2($Length $+$ Breadth$)=$ Distance

$2(3a+2a)=1.6$km

$2\left(5a\right)=16\times 100$m

$10a=1600$

$a=\frac{1600}{10}$

$a=160m$

Length $=3a=3\times 160=480$ m

Breadth $=2a=2\times 160=320$ m

So, Area of the rectangle $=$ Length $\times$Breadth

$=480\times 320$

$=153600$ m

$=153.6$ km

$\therefore$ The area of the park $=153.6$ km.